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Carry out the chi-square test for the hypothesis of no difference between the self-evaluation of health for current smokers and nonsmokers.

Smokers rate their health. The University of Michigan Health and Retirement Study (HRS) surveys… 

Smokers rate their health. The University of Michigan Health and Retirement Study (HRS) surveys more than 22,000 Americans over the age of 50 every two years. A subsample of the HRS participated in the 2009 Internetbased survey that collected information on a number of topical areas, including health (physical and mental, health behaviors), psychosocial items, economics (income, assets, expectations, and consumption), and retirement.21 Two of the questions asked on the Internet survey were “Would you say your health is excellent, very good, good, fair or poor?” and “Do you smoke cigarettes now?” The two-way table summarizes the answers to these two questions.

(a) Regard the HRS Internet sample as approximately an SRS of Americans over the age of 50, and give a 99% confidence interval for the proportion of Americans over the age of 50 who are current smokers. (b) Compare the conditional distributions of self-evaluation of health for current smokers and nonsmokers using both a table and a graph. What are the most important differences?

(c) Carry out the chi-square test for the hypothesis of no difference between the self-evaluation of health for current smokers and nonsmokers. What would be the mean of the test statistic if the null hypothesis were true? The value of the statistic is so far above this mean that you can see at once that it must be highly significant. What is the approximate P-value?

(d) Look at the terms of the chi-square statistic and compare observed and expected counts in the cells that contribute the most to chi-square. Based on this and your findings in part

(b), write a short comparison of the differences in self-evaluation of health for current smokers and nonsmokers.

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